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If F(x+y) = F(x) * F(y) Given : F(3) = 729

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If F(x+y) = F(x) * F(y) Given : F(3) = 729  [#permalink]

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05 Apr 2018, 07:42
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Difficulty:

65% (hard)

Question Stats:

53% (02:39) correct 47% (02:31) wrong based on 30 sessions

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If F(x+y) = F(x) * F(y)
Given :
F(3) = 729

Find
F(1/2) +F(1) +F(3/2) = ?

A. 13
B. 27
C. 39
D. 52
E. 81

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Joined: 30 Mar 2017
Posts: 109
GMAT 1: 200 Q1 V1
Re: If F(x+y) = F(x) * F(y) Given : F(3) = 729  [#permalink]

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05 Apr 2018, 16:19
4
1
F(3) = F(3/2 + 3/2) = F(3/2) * F(3/2) = [F(3/2)]^2 = 729 --> F(3/2) = 27

F(3) = F(1 + 1 + 1) = F(1) * F(1) * F(1) = [F(1)]^3 = 729 --> F(1) = 9

F(1) = F(1/2 + 1/2) = F(1/2) * F(1/2) = [F(1/2)]^2 = 9 --> F(1/2) = 3

F(1/2) +F(1) +F(3/2) = 3 + 9 + 27 = 39

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Re: If F(x+y) = F(x) * F(y) Given : F(3) = 729  [#permalink]

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05 Apr 2018, 07:58
3
1
IMO C.

Nice tricky Q.
F(3/2) = F(1 + 1/2) = F(1)*F(1/2) .. similarly F(1) = F(1/2)*F(1/2)

So question can be restated as ... What is F(1/2) + F(1/2)^2 + F(1/2)^3

Now we need to simplify the given info.
F(3)
= F(1+2) = F(2)*F(1) = F(1)*F(1)*F(1) ...F(2) = F(1+1) = F(1)*F(1)
=729

F(1)^3 = 9^3 (...729)
F(1) = 9
F(1) = F(1/2 +1/2) = F(1/2)^2 =9
F(1/2) = 3. I am discarding the negative roots based on the answer choices... As all are positive !

So..
Question is :
3 + 3^2 + 3^3 = 3 + 9 + 27 = 39.

Hence Option (c) is our answer.

Best,

gmatbusters wrote:
If F(x+y) = F(x) * F(y)
Given :
F(3) = 729

Find
F(1/2) +F(1) +F(3/2) = ?

A. 13
B. 27
C. 39
D. 52
E. 81

_________________
Regards,

“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)
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Re: If F(x+y) = F(x) * F(y) Given : F(3) = 729  [#permalink]

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05 Apr 2018, 09:06
gmatbusters wrote:
If F(x+y) = F(x) * F(y)
Given :
F(3) = 729

Find
F(1/2) +F(1) +F(3/2) = ?

A. 13
B. 27
C. 39
D. 52
E. 81

from this equation we can tell that
$$F(x) = (F(1)) ^n$$
F(3)=F(1)^3
F(1)=9
$$F(1/2)=F(1)^1/2$$=3
$$F(3/2)=F(1)^3/2$$=27

39
option C
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Re: If F(x+y) = F(x) * F(y) Given : F(3) = 729  [#permalink]

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18 Feb 2020, 01:52
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Re: If F(x+y) = F(x) * F(y) Given : F(3) = 729   [#permalink] 18 Feb 2020, 01:52
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